Question 163
Determine whether or not it is possible to partition the set of positive integers in infinite subsets $A_1, A_2, \dots$ such that for every positive integer $k$, the sum of elements of $A_k$ is $k + 2023$.
*Remark*: a partition of a set $X$ is a collection of subsets of $X$ such that every element of $X$ is contained in exactly one the subsets.
*Remark*: a partition of a set $X$ is a collection of subsets of $X$ such that every element of $X$ is contained in exactly one the subsets.